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Problem of the Week 1012

Unusual Four Squares Examples

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An old theorem states that every positive integer is a sum of four squares. How many integers are the sum of the squares of their four smallest positive divisors (1 is included as a divisor)?

Source: Iranian Olympiad, 98-99 Crux April 2004

© Copyright 2004 Stan Wagon. Reproduced with permission.

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8 September 2004